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 July 2007 The Search for Persistence The Real Point of the Quantitative Models
Value investors seek potential investments with features that suggest they're undervalued. Where do they look? At those that have worked in the past. Growth investors seek stocks or funds that share characteristics with those that have exhibited above average earnings or share price appreciation in the past. Those same characteristics should suggest similar performance in the future.
And that's really what most investment evaluation boils down to: Whatever characteristics have indicated above average performance in the past should continue to do so in the future. It doesn't matter if you're a value or growth investor, if you can find investments with those same features, they should reward you again in the future. What everyone is looking for is persistency. Once you isolate those fundamental features or market characteristics that have led to success in the past, you only need to find those investments that currently demonstrate them. Outperformance in one measurement period isn't enough, persistence across periods is what's important.
Fundamentals Aren't Enough To be sure, that's the underlying theory for most investment philosophies, particularly quantitative ones. What many fail to realize, however, is the fact that above average past performance is no guarantee of a similar result in the future. Sure, mutual fund prospectuses say this as a matter of course, but do investor's really believe it? You certainly wouldn't know by looking at how they pour into last quarter's top-performing mutual funds.
When you're searching for a good investment, you're not necessarily looking for one that did well in the past -- you can't buy that return now -- but rather one that will do well in the future. Those that have recently outperformed are a great place to start, but the question then becomes, "Can they carry that success forward into the future?" In other words, are they persistent? As an investor, you've probably heard a lot about the characteristics of successful investments, but you've probably not heard much at all about persistence. That may be changing.
Arcane Statistics
As an investor, you probably know that an investment with a high alpha (value added), low standard deviation (risk) and high correlation to the relevant market index is a good vehicle to use to "beat the market". What you may not know is how much of its past performance will be carried over to the future. If you see the value in alpha, beta, standard deviation, and correlation, it's high time you met the Hurst Exponent and the V-Statistic. These are measures of an asset's performance persistency and can help you make judgments about the future based on past history. When all's said and done, regardless of how you evaluate an investment, you're want to purchase those that have the greatest potential to outperform while avoiding those that are expected to trail a passive market index. If you can find those that can carry past success over into the future -- those whose superior performance can persist -- you can "beat" the market. The Hurst Exponent is a potential means of measuring an investment's performance persistency while the V-Statistic is a gauge of its duration. We call them "potential" means because like all statistics, there is plenty of margin for error and uncertainty about their ultimate reliability. In fact, there's probably more in their case than in that of many other more widely known statistical measures. The Hurst Exponent has a number of uses in a variety of areas ranging from hydrology to cardiology. In finance, many believe it can serve as a statistical measure of performance persistence, which of course, is the purpose here. The statistic gets its name from Harold Edwin Hurst (1880-1978), a British hydrologist who spent years studying flooding patterns of the Nile River. The goal was to design reservoirs that would not run out of water during the dry seasons yet not overflow during floods. Hurst observed that years with heavy flooding were often followed by additional years of flooding, yet dryer years tended to be followed by other dry years. This led him to question if there was some “memory” to this sequence and if so, could it be measured. All else being equal, one would not expect there to be a connection between one year’s floods and the next year’s weather, just one would not suppose a connection between one day’s share price movement and the next. Instead, the sequence is typically considered random, what scientists call Brownian motion. Yet just as there are periods when the Nile floods appear related, some stocks' daily share prices also seem to demonstrate an ongoing relation. Hurst used his 800-years worth of Nile data to develop a statistical calculation to estimate this autocorrelation, and now some investors are using it to gauge share price persistence. There are a number of ways to find the Hurst Exponent, but Hurst’s original – the Rescaled Range Method, often abbreviated R/S – is the most frequently used. It’s often said that you don’t actually calculate the Hurst Exponent, you estimate it. The process requires large data sets such 800-years worth of flooding data or years of closing stock prices. Without going into too much more detail (go here if you do want a thorough explanation), the Hurst Exponent (H) ranges from 0 to 1. A sequence displaying random (Brownian) motion will have a value of H = 0.5. Values below that suggest the sequence is “mean-reverting” or “anti-persistent”, meaning a movement in one direction tends to be followed by a movement in the opposite. Values above 0.5 suggest there is a degree of autocorrelation and the sequence is said to be “trend-reinforcing” or “persistent” series. Obviously it’s those values above 0.5 that are of interest here.
Presumably, the greater the Hurst value rises over 0.5, the greater the persistence in the series. Observations of persistent series suggest their persistence decays over time. That’s why Hurst observed several years of flooding followed by several dry years. It’s also why stocks don’t always move in the same direction day after day, year after year. The “V-statistic” is a measure of the duration of the decay. Hurst defined it as:  Where: (R/S)n = Rescaled Range calculation for time period n When this is plotted against the log of n, an upwardly sloping line indicates a persistent series, and the distance it travels before flattening out or turning downward is an indication of the length of its persistence. Don’t worry, you won’t have to calculate it, but you will see some graphs illustrating it.
Evaluating the Quant Models P3 and P4 were launched on July 1, 2000, so through May 31, 2007, they have 1736 trading days worth of data. P5’s inception date is January 1, 2002, giving it 1361 trading days while P6 (January 1, 2004) has 857 trading days. This is the type of calculation where more data is better than less, so we used both the longest periods for each as well as the common period (857 days) for all. The results are given in Chart 1. It’s hard to say they were surprising because it’s hard to know what to expect. The data did provide a good example of why the Hurst Exponent is estimated rather than precisely calculated. Our results varied depending on the period observed. This is clearly illustrated on Chart 2 which compares Hurst Exponents measured from inception to the value for the common period of 857 trading days. Both were calculated in the same manner, using 250 days as the base period and then 1 day increments. As you can see from Chart 2, when measured from inception, P3-P5 all had values above 0.5 suggesting there was a certain degree of persistence in performance. On the other hand, when measured over the common period, all of the models displayed “anti-persistent” behavior. Clearly the measurement period mattered.
These results are not contradictory, however, because persistence is thought to decay over time. (Think of it as the ripples emanating from a stone thrown in a calm pond: They continue in the same direction as they head toward shore, but they decrease in magnitude until they ultimately fade away.) One might conclude the persistence detected in the longer time frames had dissipated in the last 857 trading days. The V-statistic seems to support this. P4 had the highest Hurst value from inception (0.6986). The graph of its V-Statistic (Chart 3) rose sharply from November 19, 2002 through May 16, 2006. After that point, however, the graph levels off and then turns downward suggesting its persistence has completely decayed. This is the period falling within the last 857 trading days. Graphs of P3 and P5’s V-statistics have similar patterns. This again is consistent with the difference in their estimated Hurst Exponents. Given its short trading history, there is no similar comparison for P6, the data indicate it’s always been mean-reverting.
Valuable? Maybe On the other hand, P4 did display a persistent trend for just under 900 trading days suggests it is capable of such behavior for prolonged periods of time. Evidently it’s not in such a period now, but it might again be sometime in the future. In other words, its algorithm is apparently capable of creating portfolios with relatively long-term persistence. That’s good to know. In fact, that’s about all an investor can hope for. A Hurst Exponent above 0.5 suggests returns are persistent, but not that the trend will last forever. Quite the contrary, it is expected to decay over time. The best an investor can do is locate those investments currently enjoying a winning trend, and then ride them for the duration. A final thing to bear in mind is that trends go in both directions. P3 and P4 were in a definite trend in 2001 and 2002: down. The very fact that returns are persistent isn’t sufficient in and of itself to recommend an investment, unless you’re also willing to short it. Search this site! Just enter you key word or words: Get current quotes or follow your own custom portfolio,
courtesy of E-Line Financials:
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EGARDLESS OF WHAT YOUR investment style is, you're probably doing one thing: Searching for stocks or funds that have the features that suggest ongoing consistent performance. In other words, however you do it, you're searching for persistence.
